PRELIMINARY REPORT ON SODIUM TEMPERATURE COEFFICIENTS IN LARGE FAST REACTORS

Present practice in fast reactor design is to eliminate any known positive temperature coefficients of reactivity. This approach has been feasible for the fast power reactors now being constructed. In recent considerations of advanced fast reactor designs at APDA, some cases were encountered in which the sodium temperature coefficient of reactivity was positive. Because of the serious implications of this result. a study of the sodium temperature coefficient of a design in which the problem appears to be most severe was made. The principle objective of the study was to obtain a better understanding of the problem. Simply stated, reducing the sodium density causes spectral reactivity effects which can, in some situations, be positive and larger in magnitude than the negative leakage effect, thereby causing a positive temperature coefficient of reactivity. In addition. some attention was also given to possible methods of influencing the sign of the sodium coefficient. Although the results indicate that these methods couid be successfully applied. there are penalties involved with their use. The results given are believed to be quaiitatively correct, but the uncertainties in the cross section data on which they are based cast some doubt on the quantitative accuracy. (auth

The cylindrical cell approximation in thermal utilization

In solving the neutron diffusion equation in one cell of an infinite lattice, a common procedure is to replace the rectangular (or hexagonal) cell with an equivalent cylindrical cell. In order to estimate the effect of this approximation a new method is presented in which the flux in the entire cell (not the equivalent cylindrical cell) is expanded in a Fourier cosine series. Then the boundary conditions over the cell surface are satisfied exactly. Furthermore, algebraic equations for the expansion coefficients of the flux are obtained because the integrals over the cell can be done in closed form. It is found that truncation of the flux series after 10 terms gives good results. The method is felt to have more general application than to the actual problem treated here since such `mixed geometry' problems frequently arise in reactor physics and in other areas as well.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/33375/1/0000773.pd

Kinetics of active surface-mediated diffusion in spherically symmetric domains

We present an exact calculation of the mean first-passage time to a target on the surface of a 2D or 3D spherical domain, for a molecule alternating phases of surface diffusion on the domain boundary and phases of bulk diffusion. We generalize the results of [J. Stat. Phys. {\bf 142}, 657 (2011)] and consider a biased diffusion in a general annulus with an arbitrary number of regularly spaced targets on a partially reflecting surface. The presented approach is based on an integral equation which can be solved analytically. Numerically validated approximation schemes, which provide more tractable expressions of the mean first-passage time are also proposed. In the framework of this minimal model of surface-mediated reactions, we show analytically that the mean reaction time can be minimized as a function of the desorption rate from the surface.Comment: Published online in J. Stat. Phy

Singular integral equations on closed contours. II

Singular integral equations defined over closed contours in the complex plane were treated in a previous paper by a generalization of the orthogonality method introduced into transport theory by Kuščer, McCormick and Summerfield. In this paper, we show how in some cases the solutions described in the previous work may be evaluated analyticall